A new universal resample-stable bootstrap-based stopping criterion for PLS component construction |
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Authors: | Jérémy Magnanensi Frédéric Bertrand Myriam Maumy-Bertrand Nicolas Meyer |
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Institution: | 1.Institut de Recherche Mathématique Avancée, LabEx IRMIA, Laboratoire de Biostatistique et Informatique Médicale, EA3430,Université de Strasbourg et CNRS,Strasbourg,France;2.Institut de Recherche Mathématique Avancée, UMR 7501, LabEx IRMIA,Université de Strasbourg et CNRS,Strasbourg,France;3.Laboratoire de Biostatistique et Informatique Médicale, LabEx IRMIA, EA3430, Faculté de Médecine,Université de Strasbourg,Strasbourg,France |
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Abstract: | We develop a new robust stopping criterion for partial least squares regression (PLSR) component construction, characterized by a high level of stability. This new criterion is universal since it is suitable both for PLSR and extensions to generalized linear regression (PLSGLR). The criterion is based on a non-parametric bootstrap technique and must be computed algorithmically. It allows the testing of each successive component at a preset significance level \(\alpha \). In order to assess its performance and robustness with respect to various noise levels, we perform dataset simulations in which there is a preset and known number of components. These simulations are carried out for datasets characterized both by \(n>p\), with n the number of subjects and p the number of covariates, as well as for \(n<p\). We then use t-tests to compare the predictive performance of our approach with other common criteria. The stability property is in particular tested through re-sampling processes on a real allelotyping dataset. An important additional conclusion is that this new criterion gives globally better predictive performances than existing ones in both the PLSR and PLSGLR (logistic and poisson) frameworks. |
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